Daily Rambam · Expert – Beit Midrash Analysis · Standard
Mishneh Torah, Sabbath 28
Sugya Map
The core of Halachic cartography in Mishneh Torah, Sabbath 28 lies in the conceptual transformation of geographic reality into a stylized halachic jurisdiction. The sugya of Ibur Ha'ir (the "pregnancy" or expansion of a city's boundaries) and Techum Shabbat (the Sabbath boundary) addresses how human habitation projects a legal zone of "permanence" onto the natural landscape, and how that zone is measured.
[Core City Center]
│
(Within 70 2/3 Cubits)
│
[Peripheral Structure] (Must be 4x4 cubits + fit for habitation)
│
┌─────────────┴─────────────┐
[Joined to City] [Not Joined]
(Extends Techum) (e.g., Empty grave, unroofed 2-wall structure)
│
[Squaring the Boundary]
(Construct imaginary square
aligned to compass directions)
│
[Measure 2,000 Cubits outward]
(Using 50-cubit flax rope)
The Core Issues
- The Mechanism of Annexation (Ibur): How close must an isolated structure be to a city to lose its independent identity and merge into the urban collective?
- The Definition of a "Dwelling" (Dirat Keva vs. Dirat Ara'i): What structural and functional criteria must a building meet to project a seventy-cubit halachic field?
- Geometric Squaring (Ribu'a): Why and how do we transform circular, triangular, or L-shaped cities into perfect squares aligned to the cardinal directions?
- The Physics of Measurement (Havla'ah): How do we apply a physical, fifty-cubit rope to a non-Euclidean landscape of crevices, mountains, and rivers without compromising halachic precision?
The Nafka Minot (Practical Halachic Ramifications)
- The Techum boundary of peripheral residents: Do residents of a house located seventy cubits outside a city measure their 2,000 cubits from their own doorway, or do they gain the entire city's area plus 2,000 cubits from the opposite side?
- Inter-municipal transit on Shabbat: If two towns are separated by less than 141 1/3 cubits, can the residents of Town A walk through the entirety of Town B and then walk an additional 2,000 cubits beyond Town B?
- Landscape-defying boundaries: If a deep valley or steep mountain lies within the 2,000-cubit line, does the traveler measure along the undulating topography (which shortens the linear distance they can travel) or do they "span" the gap (havla'ah), treating the mountain or valley as non-existent?
Primary Source Trajectory
- Mishnaic Foundations: Mishnah Eruvin 5:1 (measuring the techum), Mishnah Eruvin 5:2-3 (triangulated villages and L-shaped cities), Mishnah Eruvin 5:4 (measuring with a fifty-cubit rope).
- Talmudic Discussion: Eruvin 55b (defining qualifyable structures), Eruvin 57a (squaring the city), Eruvin 58a-b (the mechanics of spanning crevices and mountains).
- Codification: Mishneh Torah, Sabbath 28.
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Text Snapshot
To understand the mechanics of halachic annexation, we must scrutinize the Rambam's opening formulation in Mishneh Torah, Sabbath 28:1:
"כָּל בַּיִת שֶׁהוּא חוּץ לַמְּדִינָה, אִם הָיָה בֵּינוֹ וּבֵין הַמְּדִינָה שִׁבְעִים אַמָּה וּשְׁנֵי שְׁלִישֵׁי אַמָּה—שֶׁהוּא צֶלַע בֵּית סָאתַיִם הַמְרֻבַּעַת—אוֹ פָּחוֹת מִזֶּה, הֲרֵי זֶה מִצְטָרֵף לַמְּדִינָה וְנֶחְשָׁב מִמֶּנָּה."
Grammatical & Conceptual Nuances
- "שֶׁהוּא צֶלַע בֵּית סָאתַיִם הַמְרֻבַּעַת" (Which is the side of a square Beit Satayim): The Rambam does not merely state the measurement (70 2/3 cubits) as an arbitrary decree. He anchors it in the geometric dimension of a square Beit Satayim—the area of the Tabernacle's courtyard ($50 \times 100 = 5,000$ square cubits). The square root of 5,000 is approximately 70.71 (or $70$ and $5/7$ cubits). The Rambam's use of "seventy and two-thirds" ($\approx 70.667$) is a pragmatic Rabbinic approximation, noted as such in his Commentary on the Mishnah[^1]. This choice of words signals that the seventy-cubit buffer zone is not a localized, ad-hoc leniency, but a spatial unit derived from the archetypal human courtyard (the Mishkan).
- "הֲרֵי זֶה מִצְטָרֵף" (Behold, it joins): The verb mitztaref (conjugating in the reflex-passive Nitpa'el) implies an automatic, ontological merger. The house does not merely extend a municipal line; it is absorbed into the city's legal identity.
Let us contrast this with the Rambam’s language regarding transient structures in Mishneh Torah, Sabbath 28:10:
"יוֹשְׁבֵי צְרִיפִין, אֵין מוֹדְדִין לָהֶם אֶלָּא מִפֶּתַח בָּתֵּיהֶן... וְאִם יֵשׁ שָׁם שָׁלֹשׁ חֲצֵרוֹת שֶׁל שְׁנֵי שְׁנֵי בָּתִּים, הֻקְבְּעוּ כֻּלָּם."
- "הֻקְבְּעוּ כֻּלָּם" (They are all established): The root קב"ע (permanence/fixing) is the antithesis of the tzrifin (reed huts). The transition from a series of temporary, disconnected shelters to a singular, cohesive halachic "city" requires a catalyst: "three courtyards of two houses each." The word hukbe'u indicates that the permanent structures cast their quality of keva (permanence) onto the adjacent transient huts, retroactively transforming the entire encampment into a unified municipality.
Readings
Reading A: The Ohr Sameach’s Reconstruction of the Yerushalmi: Karpef as a Spatial Extension vs. Conceptual Annexation
In his commentary on Mishneh Torah, Sabbath 28:1, the Ohr Sameach[^2] addresses a fundamental dispute in the Jerusalem Talmud[^3] regarding the source and nature of the seventy-and-two-thirds cubit buffer zone (karpef).
The Yerushalmi records a dispute between Rabbi Meir and the Sages:
"רב חונה... ר"מ ורבנן מקרא אחד דורשין. ר' מאיר דרש מקיר העיר. מה ת"ל וחוצה. מכאן שנותנין קרפף לעיר... רבנן דורשין וחוצה מה ת"ל מקיר העיר... אלא מיכן שנותנין [עיבור] לעיר."
The Ohr Sameach unpacks this dispute with remarkable analytical precision. He asks: Is the seventy-cubit zone an inherent feature of any city (an automatic spatial extension), or is it only generated when there is a physical structure outside the city that needs to be annexed?
Rabbi Meir's View:
[City Wall] ─── (70 2/3 Cubits - Automatic Karpef) ───► [Techum Starts Here]
The Sages' View (as read by Ohr Sameach):
[City Wall] ─── (70 2/3 Cubits - Only if a house exists here) ───► [House Annexed] ──► [Techum]
According to Rabbi Meir, the verse in Numbers 35:4 ("from the wall of the city and outward") teaches that we grant a karpef (a seventy-cubit buffer) to every city automatically, even if it stands entirely isolated in the desert. The techum of 2,000 cubits only begins after this seventy-cubit zone.
The Rabbis (Sages), however, expound the verse to teach Ibur—the law of annexation. They hold that an isolated city does not receive an automatic seventy-cubit extension. The seventy-cubit zone only exists as a "bridge" to span the gap between the city wall and an adjacent house. If a house stands within seventy cubits, the city's boundary is extended to that house. If no such house exists, the 2,000 cubits are measured directly from the city wall.
The Ohr Sameach notes that the Babylonian Talmud[^4] appears to rule like Rabbi Meir, granting a karpef to an isolated city. However, the Rambam in his Commentary on the Mishnah[^5] and here in the Mishneh Torah appears to adopt a hybrid position. The Rambam only mentions the seventy-cubit measurement in the context of annexing an adjacent house ("Whenever there is a home... seventy and two thirds cubits or less from the city, it is considered to be part of the city").
The Ohr Sameach resolves this by analyzing the Tosefta[^6]:
"כמה יהיו קרובות לעיר ויהיו מתעברין עמה. שבעים אמה ושיריים על שבעים אמה ושיריים שהן קמ"א אמה ושליש..."
Why does the Tosefta double the measurement to $141 \ 1/3$ cubits? The Ohr Sameach explains that when two cities face each other, each city projects its own seventy-cubit karpef field. When these fields touch or overlap (i.e., when the distance between the cities is $70 \ 2/3 + 70 \ 2/3 = 141 \ 1/3$ cubits), the two cities merge into a single halachic metropolis.
The Ohr Sameach's chiddush is that the seventy-cubit zone is not an arbitrary spatial "gift." It is a gravitational field of human habitation. A single house within seventy cubits is pulled into the city's "gravitational pull." When two cities are within 141 1/3 cubits, their gravitational fields lock together, creating a unified halachic entity. If there is no second city and no peripheral house, there is no "gravitational pull" to project, and the measurement begins from the wall itself (according to the strict reading of the Sages).
Reading B: The Ra'avad's Stricture on Unresolved Talmudic Queries: The Status of Two-Walled and Roofed Structures
In Mishneh Torah, Sabbath 28:2, the Rambam codifies a list of peripheral structures that qualify as "dwellings" to extend the city's boundary:
"...synagogue that has a dwelling... a structure four cubits by four cubits that has three walls but no roof, watchtowers... a structure with two walls and a roof..."
The Ra'avad[^7] immediately launches a fierce critique of the Rambam's inclusion of "a structure with two walls and a roof" (tariq):
"אמר אברהם: זה תיקו בגמרא ולא ידענו למה פשט אותו להקל." (Says Abraham: This is left as an unresolved 'Teyku' in the Gemara, and we do not know why he resolved it leniently).
The Gemara in Eruvin 55b raises several queries regarding structures that lie on the boundary of acceptability. Among them:
- A structure with three walls and no roof (ba'ei d'lo eitfta).
- A structure with two walls and a roof (tariq).
The Gemara leaves these queries in a state of Teyku (unresolved). Under the standard rules of halachic decision-making, a Teyku in a Rabbinic law (Safek d'Rabbanan) is resolved leniently (l'kula). Since Techum Shabbat is a Rabbinic prohibition (as the Rambam himself codifies in Halacha 19), we should rule leniently and include these structures.
Why, then, does the Ra'avad object?
The Ra'avad's underlying chakira (conceptual inquiry) is: What is the nature of the leniency of Safek d'Rabbanan l'Kula in the laws of spatial boundaries?
Two Interpretations of "Safek d'Rabbanan l'Kula" in Techum Shabbat:
1. The Passive/Permissive View (Ra'avad):
We cannot actively draw a new line in space based on a doubt.
A doubt leaves the boundary unestablished.
2. The Active/Ontological View (Rambam):
Because the entire restriction of Techum is Rabbinic, any doubt
regarding the physical parameters of the boundary is resolved
by expanding the traveler's permissible range.
The Ra'avad argues that the rule of Safek d'Rabbanan l'Kula cannot be used to actively establish a positive halachic status (i.e., transforming a non-dwelling into a "dwelling" to extend a city's boundary). A doubt cannot generate a physical Ibur (annexation). If we are unsure whether a structure qualifies as a house, we cannot redraw the city's map based on that doubt. The doubt leaves the boundary unestablished; we must default to the certain, smaller boundary of the city.
The Rambam, however, holds that Safek d'Rabbanan l'Kula in Techum Shabbat operates on the final permission of movement. Since the ultimate question is "Can this person walk here on Shabbat?", and that restriction is entirely Rabbinic, any doubt regarding the physical landmarks that determine the boundary must be resolved in favor of permission[^8]. The Rambam does not view the "dwelling" status of the structure as a hard ontological reality that must be proven; rather, the structure's physical presence combined with the Rabbinic nature of techumin is sufficient to allow us to treat the space as annexed[^9].
Reading C: The Geometry of the Triangulated Villages: Maggid Mishneh, Radbaz, and the Chatam Sofer's Mathematical Realism
In Mishneh Torah, Sabbath 28:5, the Rambam codifies the complex geometric law of three villages arranged in a triangle:
[Village A (Apex)]
▲
╱ ╲
╱ ╲ (Max 2,000 cubits)
╱ ╲
╱ ╲
[Village B] ◄───┼───────┼───► [Village C]
│◄─────►│
(Max 282 2/3 cubits)
"Three villages... If there are two thousand cubits or less between the village in the middle and both of the villages on the extremities, and there are 282 2/3 cubits [or less] between the villages on the extremities, so that if the middle village were placed on the line between them, there would be 141 1/3 cubits [or less] between it and both of them, they are all considered to be a single city."
The Ra'avad again objects, arguing that the Rambam's mathematical formulation is flawed and contradicts the Gemara in Eruvin 57a. The core of the problem is the relationship between the physical distance of the triangle's base and the imaginary projection of the apex village down to that base.
The Maggid Mishneh[^10] and the Radbaz[^11] defend the Rambam by demonstrating his sophisticated grasp of geometry. The Gemara's limit of $282 \ 2/3$ cubits is precisely $2 \times 141 \ 1/3$ cubits. Why $141 \ 1/3$? Because each of the two outer villages projects a $70 \ 2/3$ cubit karpef inward. The middle village, if dropped down to the baseline, would project a $70 \ 2/3$ cubit karpef to the left and a $70 \ 2/3$ cubit karpef to the right.
Thus, the maximum gap that can be spanned between the middle village and either outer village is $70 \ 2/3 + 70 \ 2/3 = 141 \ 1/3$ cubits. If the middle village is positioned such that its virtual projection onto the baseline leaves a gap of no more than $141 \ 1/3$ cubits on either side, the entire three-village system "locks" together.
The Chatam Sofer[^12] takes this analysis a step further, addressing a critical geometric reality: What if the apex village is very far from the baseline?
The Chatam Sofer explains that the Rambam's rule is subject to a strict mathematical constraint. The physical distance from the apex village (the "middle" village in the triangle) to the two base villages cannot exceed 2,000 cubits. Why 2,000 cubits? Because 2,000 cubits is the maximum distance of a Techum. If the apex village were more than 2,000 cubits from the base, a person standing at the apex could not halachically "reach" the base to establish a unified shevitat makom (Sabbath resting place).
The Chatam Sofer’s chiddush is that the "triangulation" of cities is not a magical legal fiction; it is an application of the laws of Eruvin and physical proximity. The three villages must form a single, continuous web of human walking capability. If the apex is within 2,000 cubits, the residents of the apex can walk to the base. Once they can walk to the base, and the base villages are within the $141 \ 1/3$ cubit karpef annexation zone of the projected apex, the entire triangle is treated as a single, paved courtyard.
Reading D: Huts vs. Houses: The Metaphysics of Permanence in Halachic Urbanism
In Mishneh Torah, Sabbath 28:10, the Rambam distinguishes between permanent homes and "dwellers of huts" (yoshvei tsrifin):
"The dwellers of huts: [The Sabbath limits] should be measured from the entrance to their homes [and they do not merge into a city]... If there are three courtyards with two houses in each, [the entire area] is established [as a unit]."
The Gemara in Eruvin 59a explains that nomadic or semi-permanent dwellings (like reed huts or tents) do not possess the halachic gravity required to form a "city." They are treated as isolated individuals scattered in the field.
The Steinsaltz commentary[^13] on this halacha notes that tsrifin are "structures made of woven branches" or reeds—lacking foundation and structural density.
The analytical question is: Why does the presence of "three courtyards with two houses in each" retroactively elevate these transient huts into a unified city?
The "Keva" Catalysis:
[Tzrif (Hut)] [Tzrif (Hut)] [Tzrif (Hut)] ───► (No city status, measured individually)
[Tzrif (Hut)] ───► [Permanent House] ◄─── [Tzrif (Hut)]
│
(Cast "Keva" status over
entire neighborhood)
│
▼ ▼
[Unified City Boundary] [Unified City Boundary]
We can understand this through two distinct lomdishe models:
- The Catalytic Model: The six permanent houses (two in each of the three courtyards) act as a halachic catalyst. A "city" is defined by a minimum threshold of permanent human settlement. Once that threshold is met (six houses arranged in three courtyards), a "municipal field" is generated. This municipal field is so powerful that it expands to absorb all adjacent transient structures (tsrifin), treating them as suburbs of the primary permanent nucleus.
- The Subservience Model (Tafel): The dwellers of the huts are socially and economically dependent on the permanent residents of the three courtyards. Because the hut-dwellers rely on the permanent houses (perhaps for security, water, or commerce), their huts lose their independent, isolated status and become auxiliary structures (tafel) to the permanent settlement. Under the rule of tafel, they are integrated into the main body of the city.
The Rambam's language supports the Catalytic Model. He writes, "הוקבעו כולם" (all of them are established). The transition is not merely that the huts are "subservient" to the houses, but that the entire geographic area undergoes a metaphysical shift from ara'i (temporary) to keva (permanent).
Friction
The Kushya: The Paradox of Spanning Crevices and Mountains
In Mishneh Torah, Sabbath 28:12-13, the Rambam codifies the rules for measuring a techum when the path is interrupted by a deep crevice (gei) or a mountain:
"When [the measurers] reach a crevice that is fifty cubits [or less] wide... this should be done [by spanning], provided [the crevice] is less than four thousand cubits deep... If, however, the plumb line does not descend directly, one should not span [the crevice], unless the crevice is two thousand cubits or less in depth."
This ruling presents a massive contradiction to the Gemara in Eruvin 58b. The Gemara states:
"אמר אבימי: לא שנו אלא שאין מחיצתן מגעת לגיא, אבל מחיצתן מגעת לגיא — מבליעין אותו ואפילו עמוק מאה אמה." (Abbimi said: They only taught [the restriction on depth] when the walls of the crevice do not reach the measuring line, but if the walls reach the crevice, they may span it even if it is a hundred cubits deep).
The Ra'avad[^14] unleashes a devastating critique:
"אמר אברהם: יש כאן שיבוש גדול וערבוב דברים..." (Says Abraham: There is a great error and confusion of matters here...)
The Ra'avad points out that the Rambam's introduction of the numbers four thousand cubits and two thousand cubits for crevice depths has no source in the Talmudic text. The Gemara speaks of "a hundred cubits" or "fifty cubits." Furthermore, the Rambam's distinction between a plumb line that "descends directly" (zofet) and one that does not, and how that interacts with the depth of the crevice, seems to stand in direct contradiction to the Talmudic mechanics of havla'ah (spanning).
How could the Rambam introduce mathematical parameters (2,000 and 4,000 cubits) that appear nowhere in the sugya of Eruvin?
The Terutz: Epistemological Measurement vs. Ontological Nullification
To resolve this deep structural difficulty, we must analyze the Rambam's unique conceptualization of Havla'ah (spanning).
Let us frame the question: What are we doing when we "span" a crevice with a fifty-cubit rope?
Two Models of Havla'ah (Spanning):
Model I: Epistemological Tool (The Ra'avad's View)
[Edge A] ═════════ (50-cubit rope) ═════════► [Edge B]
│ │
▼ ▼
(Measures the true flat geographic distance.
The depth is irrelevant as long as we can span it.)
Model II: Ontological Nullification (The Rambam's View)
[Edge A] ═════════ (50-cubit rope) ═════════► [Edge B]
│ │
└───────► [Usable Space?] ◄───┘
(If the crevice is too deep, the space below
becomes halachically detached from the earth,
preventing us from "nullifying" it.)
- Model I: Epistemological Tool. The spanning of a crevice is simply a way to discover the true, horizontal distance between Point A and Point B. The physical depth of the valley is irrelevant to this measurement. As long as the rope can physically reach from one side to the other, we span it because we only care about the flat projection of the earth's surface.
- Model II: Ontological Nullification. Spanning is a halachic mechanism that nullifies the valley, treating it as if it were paved over and flat. However, this nullification has limits. If the valley is too deep, it represents a distinct, independent spatial domain that cannot be hand-waved away. It cannot be "absorbed" into the horizontal path.
The Rambam adopts Model II. He holds that the ability to nullify a crevice depends on its usability (tashmish).
The Rambam reads the Gemara in Eruvin 58b as follows:
- If a crevice has sheer, vertical walls (a plumb line descends directly), the space inside the crevice is completely unusable for normal human activity. It is "dead space." Therefore, we can easily nullify it and span it—provided its depth does not exceed 4,000 cubits. Why 4,000 cubits? Because 4,000 cubits is double the maximum techum of 2,000 cubits. If a pit is so deep that its bottom is more than 4,000 cubits away, it is halachically "detached" from the earth's surface, and we cannot span it because the rope is suspended over an infinite abyss that breaks the continuity of the land.
- If the crevice does not have vertical walls (it slopes gradually, so a plumb line does not descend directly), the slopes are physically usable for walking or storage. Because the space is usable, it possesses its own halachic reality. It cannot be easily nullified. We can only span it if its depth is 2,000 cubits or less (the single techum limit). If it is deeper than 2,000 cubits, the traveler must physically descend and ascend, measuring the actual slope, because a usable space of that magnitude cannot be bypassed via a virtual horizontal line.
Thus, the Rambam’s seemingly fabricated numbers (2,000 and 4,000 cubits) are actually brilliant, deductive applications of the core principles of Techum Shabbat[^15]. The Rambam systemizes the chaotic Talmudic measurements by linking them directly to the ultimate limits of human locomotion: the 2,000-cubit techum.
Intertext
The Biblical Prototype: Arei HaLevi'im and the Geometry of Sacred Space
The entire spatial architecture of Techum Shabbat is anchored in the biblical blueprint of the Levite Cities (Arei HaLevi'im) described in Numbers 35:4-5:
"וּמִגְרְשֵׁי הֶעָרִים אֲשֶׁר תִּתְּנוּ לַלְוִיִּם מִקִּיר הָעִיר וָחוּצָה אֶלֶף אַמָּה סָבִיב. וּמַדֹּתֶם מִחוּץ לָעִיר אֶת־פְּאַת־קֵדְמָה אַלְפַּיִם בָּאַמָּה..." (And the open land of the cities... from the wall of the city and outward, one thousand cubits round about. And you shall measure outside the city on the east side two thousand cubits...)
The Gemara in Eruvin 51a uses a Gezerah Shavah (verbal analogy) to link the "two thousand cubits" of the Levite boundary to the "place" (makom) of Shabbat in Exodus 16:29 ("Let no man go out of his place on the seventh day").
┌──────────────────────────────────────────────────────────┐
│ Levite City Spatial Divisions │
├──────────────────────────────────────────────────────────┤
│ │
│ ┌──────────────────────────────────────────────────┐ │
│ │ 2,000-Cubit Techum │ │
│ │ │ │
│ │ ┌──────────────────────────────────────────┐ │ │
│ │ │ 1,000-Cubit Migrash (Open) │ │ │
│ │ │ │ │ │
│ │ │ ┌──────────────────────────────────┐ │ │ │
│ │ │ │ City Center │ │ │ │
│ │ │ └──────────────────────────────────┘ │ │ │
│ │ └──────────────────────────────────────────┘ │ │
│ └──────────────────────────────────────────────────┘ │
└──────────────────────────────────────────────────────────┘
This biblical source establishes a tripartite division of space:
- The City Center: The zone of dense human habitation.
- The Migrash (1,000 cubits): An open, unbuilt buffer zone reserved for aesthetic green space and livestock.
- The Fields and Vineyards (2,000 cubits): The agricultural outer ring.
The Rambam’s rules of Ribu'a (squaring the city) in Mishneh Torah, Sabbath 28:7-8 are derived directly from this biblical geometry. The Torah commands us to measure the Levite boundary by "sides" (pe'ot): "the east side... the south side... the west side... the north side." This language of "sides" implies a rigid, four-sided square, aligned perfectly to the compass directions.
Even if a city is physically circular or triangular, the halakha forces us to "construct an imaginary square around it, considering it as the center of that square" (Mishneh Torah, Sabbath 28:7). We do this because the biblical prototype of human municipal space is inherently rectangular. The ribu'a process is not a mathematical convenience; it is the imposition of the divine, Tabernacle-aligned geometry of the Levite Cities onto the organic chaos of human settlement.
Shulchan Aruch and the Polish-Ashkenazic Deviation: Tur, Rama, and the Magen Avraham
The codification of these laws in the Shulchan Aruch reveals a deep rift between the Sephardic-Maimonidean tradition and the Ashkenazic-Rhenish school.
The Shulchan Aruch in Shulchan Aruch, Orach Chayim 398:5 quotes the Rambam verbatim:
"כל בית שהוא חוץ לעיר תוך שבעים אמה ושיריים... מצטרף לעיר."
However, the Rama[^16], following the Tur and Rabbenu Asher (the Rosh), introduces a major leniency that alters the entire map of Europe's Jewish quarters:
"הגה: ויש אומרים דאפילו אין שם בית אחר, נותנים לכל עיר ועיר קרפף שבעים אמה ושיריים... וכן עיקר." (Gloss: And some say that even if there is no other house, we grant to every single city a karpef of seventy and two-thirds cubits... and this is the primary ruling).
The Great Techum Split:
Rambam & Shulchan Aruch:
[City Wall] ───► (No adjacent house? Techum starts immediately at the wall)
Tur, Rama & Ashkenazic Practice:
[City Wall] ─── (70 2/3 Cubits - Automatic "Karpef" Buffer) ───► [Techum Starts Here]
This dispute traces back to our analysis of the Ohr Sameach (Reading A). The Rama adopts the view that the seventy-cubit karpef is an inherent right of any city, acting as an automatic buffer zone. Consequently, in Ashkenazic practice, the 2,000-cubit measurement always begins seventy cubits outside the city, regardless of whether there are peripheral houses.
Furthermore, the Magen Avraham[^17] on this passage addresses the definition of a "dwelling" (dirah) for the purpose of extending the city. The Rambam requires a structure of at least four cubits by four cubits. The Magen Avraham notes that each side of the building must be at least four cubits; a long, narrow hallway of $2 \times 8$ cubits (which has an area of sixteen square cubits) does not qualify.
Why? Because a "dwelling" requires the geometry of a square (meruba). A space that cannot accommodate a standard square bed and table cannot serve as the anchor for a human home, and therefore cannot project the municipal "gravitational field" of seventy cubits.
Psak/Practice
Digital Cartography vs. Chazal's Ropes: The Epistemology of Modern Techumin
In the contemporary era, the physical measurement of Techum Shabbat has been revolutionized by Global Positioning Systems (GPS), satellite imaging, and digital mapping. However, this technological precision clashes with the methodological requirements codified by the Rambam.
The Rambam in Mishneh Torah, Sabbath 28:11 states:
"אין מודדין להן אלא בחבל של חמישים אמה..." (The Sabbath limits should be measured only by using a rope of fifty cubits...)
The Measurement Dilemma:
Traditional Halachic Method:
[50-Cubit Flax Rope] ───► (Slight sag, physical pull, human margin of error)
Result: A flexible, human-scale boundary.
Modern Satellite Method:
[GPS Coordinate] ───► (Laser-precise to the millimeter)
Result: Absolute mathematical rigidity.
Why did Chazal insist on a fifty-cubit rope made specifically of flax?
- If the rope is too short (e.g., ten cubits), the measurer will pull it too tightly, stretching it beyond its true length and resulting in a techum that is too short.
- If the rope is too long (e.g., one hundred cubits), it will sag in the middle, resulting in a measurement that is too short, thereby over-restricting the traveler.
- Flax was selected because of its unique physical properties: it has minimal elasticity, ensuring consistency under tension.
This raises a profound meta-psak question: Does modern GPS measurement, which eliminates sag and elasticity, override the Rabbinic mandate to use a fifty-cubit flax rope?
The consensus of modern poskim (including the Chazon Ish[^18] and Rav Shlomo Zalman Auerbach[^19]) is that the fifty-cubit rope was a tool to achieve the closest possible approximation of 2,000 cubits in an era before advanced surveying equipment. Therefore, if we have access to more accurate scientific tools (such as laser rangefinders or satellite mapping), we may—and indeed should—use them to map the techum.
However, a critical caveat remains: We do not let scientific precision destroy the built-in leniencies of the halachic system.
The Meta-Psak of Rabbinic Leniency
The Rambam concludes this chapter with a powerful meta-halachic principle:
"...since our Sages stated that the lenient approach should be accepted in these rulings, and not the more stringent one, because the measure of two thousand cubits is a Rabbinic institution."
This principle (קל וחומר מדברי סופרים להקל) governs the entire application of modern technology to Techum Shabbat:
- If a GPS measurement shows that a peripheral house is $71$ cubits away from the city (just outside the $70 \ 2/3$ limit), but standard human measurement with a flax rope would have approximated it as within seventy cubits, we adopt the lenient human approximation.
- We accept the testimony of non-experts, servants, and even the childhood memories of adults ("We used to walk until here when I was a child") to expand the techum.
In modern practice, organizations like the Shamir Eruv Association use GIS (Geographic Information Systems) to plot a city’s techum. They construct the imaginary ribu'a (square) over the satellite map, aligning it to the true geographic north, and then project the 2,000 cubits outward.
Where the terrain is rugged, they do not need to physically perform havla'ah (spanning) with a flax rope; the software calculates the flat, horizontal distance automatically. This is halachically valid because the software's calculation achieves the exact same result that Chazal’s physical havla'ah was designed to approximate: the horizontal projection of the earth's surface.
Takeaway
Halachic geography does not merely map the physical world; it projects a human, sacred geometry onto the wilderness, transforming physical distance into a canvas of spiritual boundaries where even a single home can anchor a city.
[^1]: Rambam, Commentary on the Mishnah, Mishnah Eruvin 5:2. [^2]: Ohr Sameach, Mishneh Torah, Sabbath 28:1 s.v. "כל בית דירה כו'". [^3]: Jerusalem Talmud, Eruvin 5:2 (Halacha 2). [^4]: Eruvin 57a. [^5]: Rambam, Commentary on the Mishnah, Mishnah Eruvin 5:2. [^6]: Tosefta Eruvin 4:7. [^7]: Hasagot HaRa'avad, Mishneh Torah, Sabbath 28:2. [^8]: Maggid Mishneh, Mishneh Torah, Sabbath 28:2. [^9]: Kessef Mishneh, Mishneh Torah, Sabbath 28:2. [^10]: Maggid Mishneh, Mishneh Torah, Sabbath 28:5. [^11]: Radbaz, Mishneh Torah, Sabbath 28:5. [^12]: Chatam Sofer, Orach Chayim, Responsa 94. [^13]: Steinsaltz on Mishneh Torah, Sabbath 28:10 s.v. "צריפין". [^14]: Hasagot HaRa'avad, Mishneh Torah, Sabbath 28:12. [^15]: Maggid Mishneh, Mishneh Torah, Sabbath 28:12, explaining the Rambam's reading of Abbimi's statement in Eruvin 58b. [^16]: Rama, Shulchan Aruch, Orach Chayim 398:5. [^17]: Magen Avraham, Orach Chayim 398:6. [^18]: Chazon Ish, Orach Chayim 110. [^19]: Minchat Shlomo, Vol. I, Siman 17.
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